Sieve-Block Bootstrap sampling method for precision estimation of the time series AR model considering random errors of design matrix
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摘要: 由于传统求解时间序列自回归(auto-regressive,AR)模型的最小二乘方法无法顾及设计矩阵误差,现有的AR模型迭代解法难以应用协方差传播率给出较为精确的精度评定公式。将Block Bootstrap采样方法引入到AR模型精度评定研究中,并在其基础上借助Sieve Bootstrap的思想,定义了顾及设计矩阵误差AR模型精度评定的Sieve-Block Bootstrap采样方法。根据不同的分块准则和采样策略,本文给出了4种方法的重采样步骤。模拟实验研究分析表明,精度评定的Sieve-Block Bootstrap采样方法能够得到比最小二乘法、经典的AR模型迭代解法更加可靠的自回归系数标准差,具有更强的适用性。同时北斗卫星精密钟差真实案例表明,本文所给出的Sieve-Moving Block Bootstrap法、Sieve- Nonoverlapping Block Bootstrap法、Sieve-Circular Block Bootstrap法以及Sieve-Stationary Block Bootstrap法的均方根(root mean square,RMS)相比于总体最小二乘的RMS分别减小了70.25%、78.65%、70.89%和79.24%;进一步验证了本文算法的有效性和可靠性,为时间序列AR模型的精度评定问题提供了一种采样思路。
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关键词:
- 时间序列 /
- AR模型 /
- 精度评定 /
- Block Bootstrap方法 /
- Sieve Bootstrap方法
Abstract: Objectives: Since the traditional least square method cannot take into account the random errors of design matrix when solving the time series AR (Auto-Regressive) model. In addition, it is difficult for the existing iterative method of AR model to use the propagation of variance and covariance to give the accurate precision estimation formula. Methods: This paper introduces the Block Bootstrap resampling method into the precision estimation research of the AR model, and on the basis of it, the principle of the Sieve Bootstrap is introduced. This paper defines the Sieve-Block Bootstrap sampling method for precision estimation of the AR model considering random errors of design matrix. According to the different blocking criteria and sampling strategies, this paper gives four detailed resampling procedures. Results:The real case of BeiDou Global Navigation Satellite System satellite precision clock offsets shows that the root mean square (RMS)of the Sieve-Moving Block Bootstrap method, Sieve-Nonoverlapping Block Bootstrap method, Sieve-Circular Block Bootstrap method and Sieve-Stationary Block are given in this paper compared with the RMS of total least squares (TLS)method, decreased by 70.25%, 78.65%, 70.89% and 79.24%, respectively. Conclusions:The experimental research and analysis show that the Sieve-Block Bootstrap sampling method can obtain more reliable autoregressive coefficient standard deviations than the least square method and the classical AR model iterative method, and it has stronger applicability. -
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